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Scalar and Vector Operations

Calculating magnitude of a vector and height

If A = (12i - 16j) and B = (-24i+10j), what is the magnitude of the vector C=(2A-B)? Answers: a) 42 b) 22 c) 64 d) 90 An archer shoots an arrow with a velocity of 45 m/s at an angle of 50 degrees with the horizontal. What is the height of the arrow at a point 150 meters downrange? Answers: a) 4.7 m b) 47.0 m c) 5

Vector Components

In 1992, Akira Matsushima, from Japan, rode a unicycle across the United States, covering about 4800 km in six weeks. Suppose that, during that trip, he had to find his way through a city with plenty of one way streets. In the city center, Matsushima had to travel in sequence 280 m north, 220 m east, 360 m north, 300 m west, 1

Electric force on an electron

What is the electric force (with direction) on an electron in a uniform electric field of strength 2780 N/C that points due east? Take the positive direction to be east.

Vectors: A hunter aims directly at a target; by how much will he miss the target?

A hunter aims directly at a target (on the same level) 103 m away. If the bullet leaves the gun at a speed of 255 m/s, by how much will it miss the target? I'm assuming that the bullet will miss the target because it arcs down toward the ground as it moves horizontally. But don't I need to know how far off the ground it is in

Subtracting vectors

"The figure below (please see attached Word file) shows three vectors of lengths A = 67.8, B = 39.5, and C = 47.0. The angles are theta(a) = 28.8° and theta(b) = 54.5°, and C points along the negative y-axis. Determine the length of the vector A - C." The book indicates that the equation for subtraction of vectors is si

Components of a vector and unit vectors

While exploring a cave a woman starts at the entrance and moves the following distances. She goes 75.0m north,250m east, 125m @an angle of 30 degrees north of east and 150m south. Find the resultant displacement from the cave entrance.

Components of a vector for a golfer on the green

A golfer on the green takes three strokes to sink the ball. The successive diplacements are 4.00m to the north, 2.00m north east and 1.00m at 30 degrees west of south. Starting at the same initial point, an expert golfer could make the hole in what single-displacement?

Center of Mass

Determine the position of the center of mass of a solid triangular pyramid with vertices at (0; 0; 0), (1; 0; 0), (1; 1; 0), and (1; 1; 2).

Getting used to vectors with this problem.

Three vectors have the same length (L) and form an equilateral triangle. Find the magnitude and direction of the vectors: (a)A+B (b)A-B (c)A+B+C (d)A+B-C. Please see attachment below for figure.